Continuum robots are well suited for gentle manipulation because of their inherent compliance and ability to adapt to complex environments. However, their continuously deformable structure makes accurate configuration estimation challenging, particularly when external vision systems are unavailable or obstructed. In this work, we present an embedded pose sensing framework that combines inertial measurement units (IMUs) and active magnetic fields to estimate the robot configuration without relying on external cameras. The angular measurements from the IMU and magnetic-field references are fused to improve local orientation estimation and reduce accumulated orientation error during operation. This pose sensing scheme achieves an update rate of 16.7~Hz, allowing real-time feedback. The proposed system is experimentally validated through closed-loop control, where the estimated robot configuration is used to maintain the end-effector at a desired position while interacting with an object. These results demonstrate the potential of distributed magnetic--inertial sensing for real-time pose estimation and closed-loop control of continuum robots.
Figures & tables
Fig. 1: Modular tendon-driven continuum robot and sensing principle. a) Pose estimation during 3D curling. Frontal images show the physical robot, while isometric views highlight the reconstructed three-dimensional backbone. Orange denotes our estimate and black denotes motion-capture ground truth. b) Modular platform design and sensing principle. Relative motion between identical segments is modeled using virtual pivots, with relative positions inferred from magnetic fields generated by embedded PCB coils. c) Grasping demonstration with a soft, deformable object (T-shirt).
Fig. 2: Overview of the mechanical and electronic components of one proprioceptive module of the continuum robot. a) Exploded view of a single module. Numbered parts include (1) PCB (2) coil (3) module (4) support standoff (5) M2-20mm screw (6) M2 nut. b) Customized sensing boards in each module and customized coil.
Fig. 3: Sensing principle, data collection setup, and sampled pose distribution. a) Joint bending and magnetic sensing under the fixed pivot assumption of [ 13 ] . The IMU and magnetometer on the upper segment are assumed to move along a hemispherical surface at a fixed radius from a virtual pivot at the center of the compliant joint. b) Data collection setup using two cameras to track a world reference tag and a joint tag attached to the upper segment. The world tag provides a common reference frame, allowing the joint position to be measured when its tag is visible to either camera. Random target orientations guide sampling across the reachable workspace to learn the mapping from magnetic measurements to joint position. c) Sampled pose distribution showing (i) positions across the hemispherical workspace, (ii) a fitted spherical surface with an RMSE of 0.19 mm, supporting the fixed pivot assumption, and (iii, iv) histograms of colatitude and azimuth, respectively. Sampling covers the workspace, although hardware biases and differences between camera measurements may contribute to uneven coverage.
Fig. 4: Pose estimation during a) planar curling, b) obstacle contact, c) free 3D curling, and d) manual manipulation. Panels (i) to (iv) show selected robot configurations and the corresponding estimated backbones. Panel (v) shows instantaneous backbone RMSE against motion capture, with errors at the final frame annotated. The fused estimate (our estimation) is shown in orange, the magnetic estimate as a dashed line, constrained acceleration with quaternions as a dash dotted line, and acceleration alone as a dotted line. Motion capture is shown in solid black.
Backbone RMSE (mm)
Drift (mm/50 s)
Method
2D curl
2D obst.
3D curl
3D hand
Avg.
Cyclic
Hold
Fusion (this work)
7.6±1.1
11.3±1.1
13.3±0.9
7.8±4.0
10.0±3.2
4.1
1.2
Magnetics only
36.9±2.2
18.0±1.5
29.4±0.9
14.1±2.7
24.6±9.5
51.1
3.3
Constrained acceleration + quaternions
133.8±3.4
163.0±3.4
71.9±2.1
90.5±4.3
114.8±36.8
54.6
17.1
Acceleration only
189.0±20.4
153.8±15.3
177.7±9.1
180.8±21.1
175.3±20.7
24.5
0.3
Tip RMSE (mm)
TABLE I: Position estimation accuracy and reported drift. Scenario RMSEs are mean ± standard deviation against motion capture over five trials; Avg. reports the mean ± standard deviation across all 20 trials pooled across the four scenarios, computed from the rounded scenario statistics. Drift values are changes per 50 s averaged across x , y , and z during recordings without ground truth and may include physical motion.
Fig. 5: Task demonstrations and long-term estimation. a) Open-loop shirt grasping with grip attachments: (i) initial and (ii) final configurations. b) Height regulation at 40 mm under a 500 g tip load: (i–ii) configurations before and after loading; (iii) height response. Blue and orange dots mark the illustrated frames; the red dashed line marks load application. For this demonstration, we removed the end module to demonstrate that the shape estimation ability is independent of the number of modules. c) Estimated displacement during (i) a stationary hold and (ii) cyclic actuation. The cyclic plot shows z displacement relative to the first cycle.
Work
L [mm]
Sensing / method
Tip error
Shape error
Baaij et al. [ 20 ]
110
3 magnetometers + magnet, NN
—
4.5% (config.)
Adamu et al. [ 21 ]
240
Hall + magnet/segment, MLP
< 5% L
max 11 mm per marker
Guo et al. [ 19 ]
—
embedded magnets + sensors
0.23–9.34 mm
—
Li et al. [ 24 ]
—
Hall + base magnet + IMUs
—
< 1 mm
Pittiglio et al. [ 25 ]
64
ball chain + Hall array
2.9% L (max 7.1%)
—
Thuruthel et al. [ 26 ]
120
cPDMS strain, LSTM
2.4±2.2 mm
—
TABLE II: Reported proprioceptive sensing accuracy. L : robot or sensed length; —: unreported. Metrics and experimental conditions differ across studies. For our work, the row averages scenario means; this work’s shape error is backbone RMSE across nine tracked segments.
Continuum robots enable smooth shape morphing and safe interaction in confined environments. However, most existing systems are task-specific and depend on external sensing infrastructure, limiting their adaptability and real-world deployment. This paper presents a self-contained modular continuum robotic platform that combines mechanical reconfigurability with onboard pose estimation. The robot is constructed from interchangeable continuum joints with analytically precomputed stiffness, allowing rapid assembly and direct programming of the robot shape. Proprioceptive sensing is achieved using magnetic sensors and a modular learning-based framework, where a single model is trained per joint and reused across configurations. The system is experimentally validated in real world, demonstrating self-sensing capabilities and adaptation without external tracking.
Continuum robots often operate in uncertain environments, where accurate state estimation is essential for safe interactions. Estimate uncertainty is inherently spatially non-uniform: confidence varies depending on where measurements are available. Global estimation accuracy is not always the top priority, but rather achieving sufficient confidence at task-relevant locations along the robot. This extended abstract introduces mechanically reconfigurable sensing enabling uncertainty-shaping in state estimation for continuum robots. We present a concept hardware design demonstrating the feasibility of longitudinal translation of a sensor within a continuum robot. We demonstrate that state estimation confidence can be reconfigured by varying the sensor location, and show a reduction of full-body shape estimation errors when sliding the sensor back and forth over time, compared to a single fixed tip sensor.
Ella Walsh, Spencer Teetaert, Eric Diller +2
University of Toronto Robotics Institute, Toronto, ON, Canada
Unlike conventional rigid-link robots defined by discrete joints, continuum robots pose a fundamental challenge for expressing their complex continuous bending configurations for closed-loop control. Several modelling approaches have been proposed for conventional continuum robots, but tensegrity-based continuum robots remain largely open. Moreover, many of these approaches assume a continuous elastic backbone and are therefore not directly applicable to tensegrity manipulators, whose bodies are networks of rigid struts and tensioned cables. This work presents a reduced-order model for shape and posture control of a tensegrity-based continuum manipulator. The manipulator is modelled as a serially connected parallel-link mechanism. The proposed method is formulated as an optimization problem that uses geometric constraints of the tensegrity structure together with information from the Inertial Measurement Unit (IMU) sensors embedded in the strut elements. To the best of our knowledge, this work presents the first experimental demonstration of a real-time IMU-based shape estimation method on a full-scale tensegrity manipulator and demonstrates posture control using a simple Proportional-Integral (PI) controller. The results show that the proposed method can estimate the shape of both single-module tensegrity structures and multi-module tensegrity manipulators from arbitrary static configurations and achieve desired postures.